### Upcoming Talks

#### Zahlentheoretisches Kolloquium

**Title:**A babystep-giantstep method for faster deterministic integer factorization

**Speaker:**Markus Hittmeir (Universität Salzburg)

**Date:**Freitag, 2. 6. 2017, 13 Uhr

**Room:**SR Analysis-Zahlentheorie (NT02008), Kopernikusgasse 24, 2.Stock

**Abstract:**

Abstract.}

In 1977, Volker Strassen presented a deterministic and rigorous algorithm for solving the problem to compute the prime factorization of natural numbers $N$. His method is based on fast polynomial arithmetic techniques and runs in time $\widetilde{O}(N^{1/4})$, which has been state of the art for the last forty years. In this talk, we discuss the core ideas for improving the bound by a superpolynomial factor. The runtime complexity of our algorithm is of the form

\[

\widetilde{O}\left(N^{1/4}\exp(-C\log N/\log\log N)\right).

\]

#### Strukturtheorie-Seminar

**Title:**Linear representations of non-commutative rational functions, free probability theory, and large random matrices

**Speaker:**Tobias Mai (Universität des Saarlandes)

**Date:**01.06.2017, 11:00c.t.

**Room:**Seminarraum AE06, Steyrergasse 30, Erdgeschoss

**Abstract:**

The concept of linear representations (aka realizations or linearizations) provides some very powerful tool to deal with non-commutative rational functions, namely elements in the universal field of fractions for the ring of non-commutative polynomials (in finitely many variables). While these methods are mostly of purely algebraic origin, they are also nicely compatible with the analytic machinery of (operator-valued) free probability. This theory and the underlying notion of free independence were invented around 1985 by D. Voiculescu, originally for operator-algebraic purposes. It can be seen as a highly non-commutative analogue of classical probability theory and has deep connections to many other fields of mathematics, especially to random matrix theory. In my talk, I will explain how this fascinating interplay leads to explicit algorithms for the computation of distributions and Brown measures, respectively, of evaluations of non-commutative rational functions in freely independent random variables. As we will see, this can be used to determine the asymptotic eigenvalue distribution of certain random matrix models. Furthermore, some concrete examples will show that these algorithms are easily accessible for numerical computations. This is based on joint works with S. Belinschi, J. W. Helton, and R. Speicher.

#### Mathematisches Kolloquium ACHTUNG - Beginnzeit wurde geändert!

**Title:**Parallelism between the growth of the known Mersenne primes and the development of informatics

**Speaker:**Prof. Dr. Attila Pethő (Universität Debrecen, dzt. TU Graz)

**Date:**Mittwoch, 31. 5. 2017

**Room:**15:30: Kaffee, Sozialraum f. Analysis u. Zahlentheorie, Kopernikusg.24/II16:00: Vortrag, Seminarraum f. Statistik (NT03098) Kopernikusg.24/III

**Abstract:**